4. Consider an infinite line charge with a charge per unit length A on the z axis. In the (ct, x, y, z) frame, the line charge is at rest, and there is no current in this frame. Answer the following. (a) Find Ę and B in this reference frame. I suggest using cylindrical spatial coordinates. = -B2 with respect (b) Apply a Lorentz transform to a frame moving at 3: to the original frame. I suggest working in SI units and using the "three- vector" form of the transformation given in problem 3 above. (c) Write the charge distribution in the original coordinate system as a o(a) using delta functions, assuming that the charge is uniformly distributed on an infinite cylindrical surface of radius ε. (d) Apply the Lorentz transform to o and ♬, noting that there is no current in the original coordinate system. What is the charger per unit length \' in this frame? What is the total current I' flowing in the 2 direction in this frame? Do these results make sense, considering what the fields are in the new frame?